A billion dollars isn't that much these days, but if I didn't just take the money and run (which I'd be tempted to do considering how I feel about the Green Party after 2000 and 2016), I'd invest it in building the party to compete at the local level where it might be possible to enact progressive reforms and push the democrats to the Left in places like the Portlands, Austin, Madison, Berkely/Oakland, etc.
This, although I’d probably pocket a good chunk of the money to invest in lab-grown meat, plant-based meat analogue supply chains, lobbying for better public transit in the Sunbelt, lobbying for more affordable electric cars, building nuclear plants, preserving/documenting indigenous cultures, etc. Things that the Green Party should prioritize but can’t really tackle as effectively as NGOs.